On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

ON DISTANCE ENERGY OF GRAPHS

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

Raman and FTIR studies of the structural aspects of Nasicon-type crystals; AFeTi(PO4)3 [A ¼ Ca, Cd]

Raman and FTIR spectra of CaFeTi(PO4)3 and CdFeTi(PO4)3 are recorded and analyzed. The observed bands are assigned in terms of vibrations of TiO6 octahedra and PO4 tetrahedra. The symmetry of TiO6 octrahedra and PO4 tetrahedra is lowered from their free ion symmetry. The presence of Fe3+ ion disrupts the Ti–O–P–O–Ti chain and leads to the distortion of TiO6 octrahedra and PO4 tetrahedra. The PO4 3 tetrahedra in both crystals are linearly distorted. The covalency bonding factor of PO4 3 polyanion of both the crystals are calculated from the Raman spectra and compared to that of other Nasicon-type systems. The numerical values of covalency bonding factor indicates that there is a reduction in redox energy and cell voltage and is attributed to strong covalency of PO4 3 polyanionin